US7870532B2 - Lithography simulation method, method of manufacturing a semiconductor device and program - Google Patents
Lithography simulation method, method of manufacturing a semiconductor device and program Download PDFInfo
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- US7870532B2 US7870532B2 US12/042,879 US4287908A US7870532B2 US 7870532 B2 US7870532 B2 US 7870532B2 US 4287908 A US4287908 A US 4287908A US 7870532 B2 US7870532 B2 US 7870532B2
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70605—Workpiece metrology
- G03F7/70653—Metrology techniques
- G03F7/70675—Latent image, i.e. measuring the image of the exposed resist prior to development
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
Definitions
- the present invention relates to a lithography simulation method.
- a first aspect of the present invention there is provided a lithography simulation method of obtaining a resist image by simulation using first and second functions, obtaining the resist image by the simulation comprising: determining a mask transmission function from a mask layout; modulating the mask transmission function using the first function to determine a modulated mask transmission function; obtaining an optical image of the mask layout using the modulated mask transmission function; and applying the second function to the optical image to obtain the resist image of the mask layout.
- a second aspect of the present invention there is provided a computer readable medium configured to store program instructions for execution on a computer, the program instructions being applied to a lithography simulation of obtaining a resist image by simulation using first and second functions, the program instructions causing the computer to perform: determining a mask transmission function from a mask layout; modulating the mask transmission function using the first function to determine a modulated mask transmission function; obtaining an optical image of the mask layout using the modulated mask transmission function; and applying the second function to the optical image to obtain the resist image of the mask layout.
- FIG. 1 is a flowchart to explain a basic procedure of a lithography simulation method according to an embodiment of the present invention
- FIG. 2 is a view to explain a basic concept of the lithography simulation method according to the embodiment of the present invention
- FIG. 3 is a view to detailedly explain part of the lithography simulation method according to the embodiment of the present invention.
- FIG. 4 is a view to explain mask topography effect according to the embodiment of the present invention.
- FIG. 5 is a view to explain mask topography effect according to the embodiment of the present invention.
- FIG. 6 is a view to explain mask function modulation according to the embodiment of the present invention.
- FIGS. 7A to 7D are views showing various test patterns for experimentally obtaining parameters according to the embodiment of the present invention.
- FIG. 8 is a flowchart to explain a method of manufacturing a semiconductor device according to an embodiment of the present invention.
- FIG. 1 is a flowchart to explain a basic procedure of a lithography simulation method according to an embodiment of the present invention.
- FIG. 2 is a view to explain a basic concept of the lithography simulation method according to the embodiment of the present invention.
- FIG. 3 is a view to detailedly explain part of the lithography simulation method according to the embodiment of the present invention.
- the lithography simulation method according to this embodiment will be explained with reference to the foregoing drawings.
- FIG. 3( b ) shows a mask transmission function in frequency domain.
- FIG. 3( c ) shows a mask transmission function in space domain.
- the mask transmission function 12 is modulated using mask transmission function modulation function (first function) to obtain a modulated mask transmission function 13 (S 3 ).
- the mask transmission function modulation function is applied to the mask transmission function shown in FIG. 3( c ) to calculate a modulated mask transmission function shown in FIG. 3( d ).
- the mask transmission function is modulated using a mask transmission function modulation function approximately reflecting the mask topography effect.
- FIG. 4 and FIG. 5 are views to explain about the mask topography effect.
- FIG. 4( a ) and FIG. 5( a ) are views schematically showing a photo mask.
- 50 denotes a photo mask
- 51 denotes an opaque area
- 52 denotes a clear area.
- FIG. 4( b ) and FIG. 5( b ) are views showing electric field distribution of light transmitting through the photo mask 50 .
- a symbol P denotes an actual electric field distribution based on mask topography effect.
- Q denotes an electric field distribution using thin mask approximation.
- the mask topography effect is largely classified into edge scattering effect, oblique effect and waveguide effect.
- edge scattering effect scattering phenomenon occurs in the electric field distribution at the boundary (edge) between the opaque area 51 and the clear area 52 of the photo mask 50 , as seen from FIG. 4 .
- the edge scattering effect occurs at all edges.
- the foregoing oblique effect and waveguide effect the following phenomenon occurs. Namely, light passing through the clear area 52 between opaque areas 51 attenuates, as shown in FIG. 5 .
- the width (space width) of the clear area 52 gradually becomes narrow, and thereby, the oblique effect and the waveguide effect increase.
- the oblique effect is a phenomenon such that light intensity attenuates at the boundary (edge) between the opaque area 51 and the clear area 52 resulting from oblique incident light (i.e., light obliquely incident on the photo mask 50 ).
- the waveguide effect is a phenomenon such that light intensity pasting through the clear area 52 attenuates.
- the width (space width) of the clear area 52 becomes narrow, and thereby, the waveguide effect remarkably appears in particular.
- the mask transmission function is modulated using mask transmission function modulation function approximately reflecting the foregoing oblique effect and waveguide effect.
- FIG. 6 is a view to explain the mask transmission function modulation function.
- the mask transmission function modulation function shown in FIG. 6 is called “exslope”.
- a mask transmission function S is differentiated to determine a function S′ (first preliminary function) expressing the gradient of the mask transmission function S.
- a function S′ first preliminary function
- the density of the mask layout increases, and thereby, the gradient of the mask transmission function S increases.
- the absolute value (amplitude level) of the function S′ increases.
- the function S′ is sliced at a predetermined level lev.
- portions Sp′ exceeding the predetermined level lev, of the function S′ are extracted. Specifically, the following relation and equation are given.
- a function ⁇ (x) (second preliminary function) is calculated based on the extracted portions Sp′ of the function S′. Specifically, convolution integral of the extracted portion Sp′ of the function S and a Gauss function having standard deviation ⁇ is made to calculate the function ⁇ (x).
- the function ⁇ (x) is a function such that the absolute value increases when the density of the mask layout increases.
- the function ⁇ (x) is applied to the mask transmission function S to modulate the mask transmission function, calculating a modulated mask transmission function S′′.
- the modulated mask transmission function S′′ is obtained from the following equation.
- S′′ S /(1+ w*f ( x ))
- w is a fitting parameter for fitting S′′ to an experimental value.
- the mask transmission function modulation function (first function) is applied to the mask transmission function 12 .
- the modulated mask transmission function 13 is calculated.
- the mask topography effect is properly reflected to the modulated mask transmission function obtained in the manner described above.
- the foregoing oblique effect and waveguide effect shown in FIG. 5 are properly reflected.
- the width (space width) of the clear area of the photo mask gradually becomes narrow, and thereby, the foregoing oblique effect and waveguide effect increase.
- the width (space width) of the clear area of the photo mask gradually becomes narrow, and thereby, a quantity of attenuation of light passing through the clear area increases.
- the width (space width) of the clear area becomes narrow in an area where the pattern density of the mask layout is high (the distance between patterns is narrow). Therefore, the pattern density of the mask layout becomes high, and thereby, a quantity of attenuation of light passing through the clear area increases.
- the mask transmission function S and the modulated mask transmission function S′′ properly reflect the relationship described above.
- the mask transmission function modulation function shown in FIG. 6 is employed, and thereby, the mask topography effect can be approximately reflected.
- the thin mask approximation model the thickness of the pattern on the photo mask is set to zero
- high-accuracy simulation is effected.
- the slice level “lev” shown in FIG. 6( a ) is properly set, and thereby, the extracted portion Sp′ shown in FIG. 6( b ) can be made zero in an area where the pattern density is low (the distance between patterns is wide).
- the function ⁇ (x) of FIG. 6( c ) is made zero in a low pattern density area.
- the “exslope” shown in FIG. 6 is used as the mask transmission function modulation function.
- the following “slope” or “double Gaussian” may be used as the mask transmission function modulation function.
- S(x, y) is a mask transmission function before modulated
- P(x, y) is a modulated mask transmission function
- ⁇ is a fitting parameter
- S(x, y) is a mask transmission function before modulated
- P(x, y) is a modulated mask transmission function
- G(x, y, ⁇ ) is a Gauss function
- ⁇ 1, ⁇ 2, w1 and w2 are fitting parameters.
- “*” expresses a convolution integral.
- An optical image of the mask layout 11 is determined using the modulated mask transmission function 13 (S 4 ). Specifically, as illustrated in FIG. 2 , an image of the mask layout 11 after passing an optical system 14 of an exposure apparatus is determined as an optical image 15 .
- the optical image 15 is defined based on light intensity distribution of light passing through the optical system 14 .
- an optical image shown in FIG. 3( e ) is calculated from the modulated mask transmission function of FIG. 3( d ).
- Partial coherent imaging expressed by the following equations (1) and (2) is usable to calculate the optical image 15 .
- I(x, y) is light intensity distribution (optical image) at a point (x, y) calculated using a thin mask approximation model
- S is intensity distribution of effective light source
- P is a pupil function of an optical system
- * is a complex conjugate
- m ⁇ is a Fourier transform of complex transmission distribution of a mask pattern
- TCC is a transfer function called as a transmission cross coefficient.
- the foregoing equation (2) is employed using a quadrupole illumination having NA of 1.0 and coherent factor of 0.95.
- the predetermined function is applied to the optical image 15 to determine a resist image 16 of the mask layout (S 5 ).
- a resist image shown in FIG. 3( f ) is calculated from the optical image shown in FIG. 3( e ).
- the resist image 16 is calculated using a model simply (approximately) expressing a reaction in a photo resist onto which exposure light is applied (reaction of acid in photo resist). “Gaussian”, “mask Gaussian” and excess acid model” are given as a model simply expressing a reaction in the photo resist.
- P(x, y) is a resist image at a point (x, y)
- I(x, y) is an optical image
- G(x, y, ⁇ ) is a Gauss function having standard deviation ⁇
- w is a fitting parameter.
- “*” expresses a convolution integral.
- P(x, y) is a resist image at a point (x, y)
- I(x, y) is an optical image
- G(x, y, ⁇ ) is a Gauss function having standard deviation ⁇
- S(x, y) is a mask transmission function
- w is a fitting parameter.
- “*” expresses a convolution integral.
- the “excess acid model” is expressed by the following equations and calculation procedures (a) to (c).
- I is an optical image
- lev is a parameter for extracting predetermined optical image intensity or more.
- G(x, y, ⁇ L) is a Gauss function having a diffusion length ⁇ L (corresponding to standard deviation), and “*” expresses a convolution integral.
- w is a fitting parameter
- the resist image 16 of the mask layout is determined in the manner described above. Then, the obtained resist image 16 is sliced at a predetermined level 17 . A slice width D obtained at that time is given as a resist pattern dimension (CD value) of the target mask layout.
- the mask transmission function is modulated using the mask transmission function modulation function (first function) approximately reflecting the mask topography effect. Then, the optical image of the mask layout is determined using the modulated mask transmission function.
- the mask transmission function modulation function first function
- the optical image of the mask layout is determined using the modulated mask transmission function.
- the preliminary function e.g., function ⁇ (x) of FIG. 6( c )
- the mask transmission function is modulated so that when the absolute value of the preliminary function increases, the absolute value decreases.
- Parameters included in the foregoing various functions are previously determined based on the following resist pattern dimension.
- the resist pattern dimension is obtained from a resist pattern of a test pattern formed by the actual lithography, or from a resist image of a test pattern obtained by a desired simulation different from the foregoing simulation of this embodiment.
- the fitting parameter is previously determined so that a resist dimension obtained by the lithography simulation of this embodiment is close to a resist dimension to be fitted as much as possible.
- the desired simulation different from the foregoing simulation of this embodiment includes simulation using strict calculation based on a strictly physical model reflecting mask topography effect.
- FIGS. 7A to 7D are views showing various test patterns for experimentally obtaining parameters.
- FIG. 7A is a view showing an isolated pattern.
- FIG. 7B is a view showing an island pattern.
- FIG. 7C is a view showing a line and space pattern.
- FIG. 7D is a view showing two lines pattern.
- L 1 to L 4 denote a line width
- S 3 and S 4 denote a space width.
- a plurality of test patterns having a different line width L 1 is prepared as a test pattern shown in FIG. 7A .
- a plurality of test patterns having a different line width L 2 is prepared as a test pattern shown in FIG. 7B .
- a plurality of test patterns having different line width L 3 and space width S 3 is prepared as a test pattern shown in FIG. 7C .
- a plurality of test patterns having different line width L 4 and space width S 4 is prepared as a test pattern shown in FIG. 7D .
- several hundreds of test patterns are prepared.
- a resist pattern dimension of each test pattern is determined using the lithography simulation method of this embodiment. Namely, the resist pattern dimension is determined using the lithography simulation method shown in FIG. 1 to FIG. 3 . Specifically, the resist pattern dimension is determined in the following manner.
- a mask transmission function of the test pattern is determined. Then, the mask transmission function of the test pattern is modulated using the first function having a first parameter before fitting. The optical image of the test pattern is calculated using the modulated mask transmission function of the test pattern. The second function having a second parameter before fitting is applied to the optical image of the test pattern to calculate a resist image of the test pattern. The resist pattern dimension (e.g., corresponding to dimension D of FIG. 2 ) of the test pattern is calculated from the resist image thus obtained.
- the following resist pattern dimensions are determined with respect to the foregoing each test pattern.
- One is a resist pattern dimension obtained by the actual lithography.
- Another is a resist pattern dimension obtained from the resist image determined using a desired simulation different from the simulation of this embodiment.
- a resist pattern dimension to be fitted is determined.
- the foregoing desired simulation includes simulation by strict calculation based on a strict physical model reflecting mask topography effect.
- the resist pattern dimension obtained by the lithography simulation method of this embodiment is compared with a resist pattern dimension to be fitted. If the comparative result satisfies a predetermined condition, the first and second parameters before fitting are determined as the final first and second parameters. Specifically, the dimensional difference is calculated between the resist pattern dimension obtained by the lithography simulation of this embodiment and the resist pattern dimension to be fitted. The first and second parameters are simultaneously determined so that the dimensional difference becomes small as much as possible. For example, the first and second parameters are determined so that RMS (Root Mean Square) of the dimensional difference becomes the minimum.
- RMS Root Mean Square
- Lithography simulation is carried out using the initial value of the fitting parameter. Then, the dimensional difference errCD is calculated between a resist dimensional value obtained by the lithography simulation and that obtained by the actual photolithography. Specifically, the RMS of the dimensional difference errCD is calculated with respect to 510 patterns (patters shown in FIG. 7 ).
- the fitting parameters are perturbed to carry out the lithography simulation, and thereby, the dimensional difference errCD is calculated. Likewise, perturbation of the fitting parameters and calculations of the dimensional difference errCD are repeated. In this way, the fitting parameter is optimized so that the RMS of the errCD becomes the minimum.
- RMS is 2.49 nm.
- the RMS is 5.5 nm.
- the fitting parameter of the first function (mask transmission function modulation function) and that of the second function (function for determining resist image) are simultaneously determined based on the following pattern dimension. It is the pattern dimension of the resist pattern of the test pattern formed by the actual lithography (or the resist pattern dimension obtained from the resist image of the test pattern determined by a desired simulation different from the simulation of this embodiment). Namely, the fitting parameter of the first function (mask transmission function modulation function) is determined based on the pattern dimension of the actual resist pattern (or pattern dimension obtained by a desired simulation different from the simulation of this embodiment), in addition to the fitting parameter of the second function (for calculating the resist image). Therefore, the actual resist dimension value (or the resist dimensional value equivalent to the actual resist dimensional value) is accurately reflected to the fitting parameters of the first and second functions. Thus, it is possible to obtain a high-accuracy simulation model.
- FIG. 8 is a flowchart to schematically explain a method of manufacturing a semiconductor device.
- a design data is prepared (S 11 ). Then, lithography simulation is carried out using the method described in the foregoing embodiment (S 12 ). Based on the guideline obtained by the lithography simulation, mask data is generated from the design data (S 13 ). Based on the generated mask data, a photo mask is produced (S 14 ). A pattern formed on the photo mask thus produced is transferred onto a photo resist on a semiconductor wafer (S 15 ). The photo resist is developed to form a photo resist pattern (S 16 ). Etching is carried out using the photo resist pattern as a mask to form a pattern on the semiconductor wafer (S 17 ).
- the method described in the foregoing embodiment is realizable by a computer whose operation is controlled by a program describing the procedures of the method.
- the foregoing program is provided via a recording medium such as magnetic disk or communication line (wired or wireless) such as Internet.
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Abstract
Description
S″=S/(1+w*f(x))
P(x, y)=S(x, y)×exp(β|g|)
g=(1/S(x, y))×((∂S/∂x)2+(∂S/∂y)2)1/2
P(x, y)=w1×G(x, y, σ1)*S(x, y)+w2×G(x, y, σ2)*S(x, y)
P(x, y)=w×G(x, y, σ)*I(x, y)
P(x, y)=I(x, y)+w×G(x, y, σ)*S(x, y)
I″(x, y)=G(x, y, ΔL)*I′(x, y)
I′″(x, y)=I(x, y)+w×I″(x, y)
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US20100081295A1 (en) * | 2008-09-30 | 2010-04-01 | Masanori Takahashi | Process model evaluation method, process model generation method and process model evaluation program |
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JP4921536B2 (en) * | 2009-10-26 | 2012-04-25 | キヤノン株式会社 | Program and calculation method |
JP5479070B2 (en) | 2009-12-17 | 2014-04-23 | 株式会社東芝 | Optical image intensity calculation method, pattern generation method, semiconductor device manufacturing method, and optical image intensity distribution calculation program |
NL2006091A (en) * | 2010-03-05 | 2011-09-06 | Asml Netherlands Bv | Design rule optimization in lithographic imaging based on correlation of functions representing mask and predefined optical conditions. |
US10671786B2 (en) * | 2016-11-29 | 2020-06-02 | Taiwan Semiconductor Manufacturing Co., Ltd. | Method of modeling a mask by taking into account of mask pattern edge interaction |
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